I have officially started my quest to rid our house of uneccessary chemicals and to strive for a more frugal and simple approach. My first two success stories are vinegar and a lemon-baking soda paste.
The vinegar was used instead of a rinse aid in the dishwasher. After the first try there was no difference in my washed dishes. The glasses still had to be polished. Since the vinegar was already in the dishwasher rinse aid compartment, the next load got the same treatment. This time however I could totally see the difference. My glasses were not covered with the usual white film of the detergent. To be honest, there doesn't seem to be a difference to the rinse aid from the store. So we'll definitely be using vinegar instead of the spendy and chemically ladden rinse aid.
The other "dirt" in our house that has been bothering me for a while were black-ish scratchmarks in our white sink. Other cleaners didn't quite get it out. The baking soda and lemon juice (real lemon) paste did a fabulous job of bleaching and cleaning it with very little effort. I let the paste sit for at least 15 minutes and then scrubbed it just a little with the scrubby side of the sponge. Works great!